Question: The equation of an ellipse $E$ is $\dfrac {(y+8)^{2}}{4}+\dfrac{x^2}{36} = 1$. What are its center $(h, k)$ and its major and minor radius?
Solution: The equation of an ellipse with center $(h, k)$ is $ \dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$ We can rewrite the given equation as $\dfrac{(x - 0)^2}{36} + \dfrac{(y - (-8))^2}{4} = 1 $ Thus, the center $(h, k) = (0, -8)$ $36$ is bigger than $4$ so the major radius is $\sqrt{36} = 6$ and the minor radius is $\sqrt{4} = 2$.